MPRAMunich Personal RePEc Archive
9/56 Year Cycle: Panics, Earthquakes,Hurricanes and Volcanoes
David McMinn
2013
Online at http://mpra.ub.uni-muenchen.de/51693/MPRA Paper No. 51693, posted 25. November 2013 16:18 UTC
1
David McMinn
Independent Scholar
www.davidmcminn.com
Twin Palms,
Blue Knob. NSW 2480.
Australia
David McMinn completed a BSc at the University of Melbourne in 1971 and
subsequently worked as a mineral economist in ANZ Banking Group Ltd (a major
Australian financial institution). Since leaving this position in 1982, he has conducted
private research on cycles, with his main interests centering on Moon Sun cycles and the
9/56 year grid. These involved new innovative concepts in cycle studies. McMinn has
published numerous papers and articles in the fields of technical analysis and seismology,
as well as three books on market timing.
2
9/56 YEAR CYCLE: PANICS, EARTHQUAKES, HURRICANES AND
VOLCANOES
Abstract: This paper explores cyclic commonalities evident in the timing of four
phenomena – financial panics, earthquakes, volcanic eruptions and Atlantic hurricanes.
Surprisingly, a 9/56 year cycle could be established for all four categories. This cycle in
turn could be strongly linked to Moon Sun tidal harmonics, which were hypothesized to
activate critical events within 9/56 year patterns. Several lunisolar cycles aligned very
closely at 9.0 and 56.0 solar years, thus providing theoretical support for a strong
lunisolar influence. How this cycle actually functioned remained a mystery, as it falls
outside prevailing paradigms in finance and the sciences. Further research breakthroughs
have the potential to greatly increase the forecasting accuracy in the fields of finance,
seismology, meteorology and volcanology. The 9/56 year cycle may show up in the
timing of other critical phenomena, although this remains to be seen.
Key words: 9/56 year, cycle, financial panics, earthquakes, hurricanes, volcanoes.
Introduction A 56 year panic cycle in US financial activity was first proposed by J M Funk (1932).
McMinn (1986, 1993, 1996) expanded upon this concept and presented a 9/56 year cycle
in the timing of major US and Western European financial crises since 1760. More
recently, a 9/56 year effect was extrapolated to major earthquakes (McMinn, 2011a,
2011b, 2011d), Category 5 Atlantic hurricanes (McMinn, 2011c), Hawaiian volcanoes
(McMinn, 2011d) and world mega eruptions (McMinn, 2012). Firm correlates could be
produced with the 9/56 year grid, after assessing historic catalogs in each of the
respective disciplines. These varied phenomena are believed to share a fundamental
cyclic principle that influences the timing of critical events, a finding that was both
remarkable and unexpected. The 9/56 year grid may be linked intimately with Moon Sun
cycles, as several lunisolar cycles aligned very closely at 9.0 and 56.0 solar years. Thus,
Moon Sun tidal harmonics are hypothesised to activate acute events that cluster within
the 9/56 year grid.
The 9/56 year cycle consists of a grid repeating the intervals 56 years vertically (called
sequences) and 9 years horizontally (called subcycles). The 56 year sequences have been
numbered in accordance with McMinn (1993), with 1817, 1873, 1929, 1985 being
designated as Sequence 01, 1818, 1874, 1930, 1986 as Sequence 02 and so forth.
McMinn (Appendix 2, 2002) presented the full numbering. The year of best fit has been
applied in the various tables. Additionally, Appendix 9 gives the essential background
information on the various Moon Sun cycles and the terms used in this paper.
Financial Crises Kindleberger (Appendix B, 1996) listed some 30 major financial panics for the USA &
Western Europe from 1760 to 1940 (see Appendix 1), of which 16 appeared in the 9/56
year grid shown in Table 1 (significant p < .001). For the period 1940-1996, numerous
international currency crises were given in Kindleberger’s listing, only two of which
3
appeared within the 9/56 year configuration. Even including these currency speculations,
21 of Kindleberger’s 44 crisis years (1760-1996) fell in the 9/56 year pattern, which was
still significant (p < .01).
The layout in Table 1 contained most of the major financial disasters in US history –
1792, 1819, 1837, 1857, 1873, 1884, 1893, 1929, 1931, 1933, 1987, 1998 and 2007.
Listings of US & Western European crises by other preeminent economists also fell
selectively in the 9/56 year cycle (see Appendix 1). Such findings offered support for a
9/56 year panic cycle in financial trends. Amazingly, this cycle has persisted for over 250
years despite the radical changes in technology, financial complexity, economic
structures and so forth.
Table 1
9/56 YEAR CYCLE: FINANCIAL PANICS 1760-1996
Year beginning March 1
Sq
52
Sq
05
Sq
14
Sq
23
Sq
32
Sq
41
Sq
50
Sq
03
Sq
12
Sq
21
Sq
30
Sq
39
Sq
48
Sq
01 1761
1763 1772 1781 1790 1799 1808 1817
1765 1774 1783 1792 1801 1810 1819 1828 1837 1846 1855 1864 1873
1812 1821 1830 1839 1848 1857 1866 1875 1884 1893 1902 1911 1920 1929
1868 1877 1886 1895 1904 1913 1922 1931 1940 1949 1958 1967 1976 1985
1924 1933 1942 1951 1960 1969 1978 1987 1996 2005 2014
1980 1989 1998 2007 2016
The 56 year sequences are separated by an interval of 9 years.
Years in bold contained major financial panics and crises listed by Kindleberger
(Appendix B, 1996).
Source: McMinn (1993, 1995).
Earthquakes
The 9/56 year grid has been correlated with an extensive range of historic seismic
catalogs by country and region (McMinn, 2011a, 2011b, 2011d). A coverage of
Californian events and world mega quakes has been presented from this body of work.
California. The US Geological Survey listed major quakes (mag ≥ 6.9) occurring in
California, Nevada and Baja California for the 1800-2000 period, with post 2000 events
being inserted by the author (see Appendix 2). This compilation gave 31 events, of
which 10 took place in Table 2 (McMinn 2011a). The table comprised five 56 year
sequences or about 9% of the complete 9/56 year grid, but it contained:
* 36% of all major Californian earthquakes (mag ≥ 6.9).
* 58% of all major Californian earthquakes taking place in October to December.
Table 2
9/56 YEAR CYCLE: MAJOR QUAKES IN
CALIFORNIA – NEVADA – BAJA CALIFORNIA 1800–2010 (mag ≥ 6.9)
4
Year beginning April 5
Sq
25
Sq
34
Sq
43
Sq
52
Sq
05
1803 + 9 1812
Dec08
Dec21
+ 9 1821
1841 + 9 1850 + 9 1859 + 9 1868
Oct21
+ 9 1877
1897 + 9 1906
Apr18
+ 9 1915
Oct03
Nov21
+ 9 1924 + 9 1933
1953 + 9 1962 + 9 1971 + 9 1980
Nov08
+ 9 1989
Oct18
2009
Aug03
2010
Apr04
Years in bold contained quakes (mag ≥ 6.9) in the year beginning April 15.
Source of Raw Data: US Geological Survey.
Source: McMinn (2011a).
Crucially, four 56 year sequences in Table 2 (Sqs 25, 34, 43 & 52) experienced many
record events in south western North America.
Sq 25 - Record Baja California quake (Mexicali. mag 7.2. Apr 4, 2010).
Sq 25 – Equal 4th
rank quake for Baja California (mag 6.9. Aug 3, 2010).
Sq 34 - Record northern Californian quake (San Francisco. mag 8.25. April 18, 1906).
Sq 34 - Record New Mexico quakes happened on July 16 and November 15 in 1906
(both mag 5.8).
Sq 43 - Record quake for Nevada (Pleasant Valley. mag 7.3. Oct 3, 1915).
Sq 43 - 2nd
rank quake for Baja California (Volcano Lake. mag 7.1. Nov 21, 1915).
Sq 52 - Record quake for Hawaii (mag 7.9. Apr 2, 1868).
Sq 52 - Record US volcanic eruption (ex Alaska) (Mt St Helens, May 18, 1980).
Additional key records fell in another 9/56 year grid presented in Appendix 3.
There were notable seasonal trends in the timing of Californian earthquakes within the
9/56 year grid. Sequences 43, 52 & 05 in Table 2 contained 7 major quakes, all of which
happened in the 2.7 months to December 21. This compared with a mere 0.5 that could
have been expected by chance. McMinn (2011a) presented other examples of this
seasonal effect.
World Mega Quakes. Fujita (2011) of the Michigan State University published a catalog
of the biggest world earthquakes for 1900–2010. From this was compiled a listing of
mega quakes (mag ≥ 8.5) (see Appendix 4), with the events of March 11, 2011 (Japan
mag 9.0) and April 22, 2012 (Indonesia mag 8.6) being inserted. These quakes aligned
5
most closely in two grids, each with 54 year intervals on the horizontal and 56 years on
the vertical (denoted as 54/56 year cycles) (see Table 3).
Table 3
54/56 YEAR CYCLES: WORLD MEGA QUAKES SINCE 1900 (mag ≥ 8.5)
Grid A
7.5 months ending March 31
Sq 29 Sq 27 Sq 25 Sq 23 Sq 21
1949
1951
1950
0815
+ 54 2005
0328
2004
1226
1953
1952
1104
+ 54 2007
1901 + 54 1955 + 54 2009
1957
0309
+ 54 2011
0311
2013
Grid B
10.5 months ending August 20
Sq
36
Sq
34
Sq
32
Sq
30
Sq
28
Sq
26
1900 + 54 1954
1902 + 54 1956 + 54 2010
0227
1904 + 54 1958 + 54 2012
0411
1906
0131
0820
+ 54 1960
0522
+ 54 2014
1908 + 54 1962 + 54 2016
1964
0328
1963
1013
+ 54 2018
Events in bold were among the top quakes (M ≥ 8.6) recorded since 1900 in the
catalog by Kazuya FUJITA.
Dates expressed as YYYYMMDD.
Source: McMinn (2011b).
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Grids A and B in Table 3 can be combined to produce a grid repeating 9, 45, 9, 45…
years on the horizontal and 56 years on the vertical (denoted as a 9-45/56 year cycle) (see
Table 4). This accounted for 25% of the complete 9/56 year grid, yet it contained all of
the top 6 world mega quakes (mag ≥ 8.8) and 11 of the top 13 mega quakes (mag ≥ 8.6).
The latter was in contrast to the 3.3 that could have been expected by chance.
Table 4
9-45/56 YEAR CYCLE: WORLD MEGA QUAKES SINCE 1900 mag ≥ 8.6
Year ending May 25
Sq
29
Sq
38
Sq
27
Sq
36
Sq
25
1908 + 45 1953
1952*
Nov04
1901 + 9 1910 + 45 1955 + 9 1964*
Mar28
+ 45 2009
1957
Mar09
+ 9 1966 + 45 2011*
Mar11
+ 9 2020
2013 2022
Continued…….
Sq
34
Sq
23
Sq
32
Sq
21
1904 + 45 1949 + 9
+ 9 1906
Jan31
+ 45 1951
1950
Aug15
+ 9 1960*
May22
+ 45 2005
Mar28
2004*
Dec26
+ 9
+ 9 1962 + 45 2007 + 9 2016
+ 9 2018
Continued…….
Sq
30
Sq
39
Sq
28
Sq
27
Sq
28
1900 + 45 1945 + 9 1954
1902 + 45 1947 + 9 1956 + 45 2001 + 9 2010*
Feb27
1958 + 45 2003 + 9 2012
Apr11
2014
Events *asterisked had magnitudes ≥ 8.8 in the 7 months to May 31.
Source of Raw Data: Kazuya FUJITA.
Source: McMinn (2011b).
Atlantic Hurricanes The timing of Category 5 Atlantic hurricanes was sourced from UNISYS (see Appendix
7
5). Tropical storms of such high intensity were not recorded before 1924, a situation that
may reflect long term trends in global warming. The intensity and frequency of Atlantic
hurricanes has increased markedly over the past century.
The 13 56 year sequences in Table 5 contained 17 Category 5 hurricanes, compared with
a total of 32 (significant p < .001).
Table 5
9/56 YEAR CYCLE: CATEGORY 5 ATLANTIC HURRICANES
1920-2010 Sq
43
Sq
52
Sq
05
Sq
14
Sq
23
Sq
32
Sq
41
Sq
50
Sq
03
Sq
12
Sq
21
Sq
30
Sq
39
1922 1931 1940 1949
1958
*
1967
*
1924
*
1933 1942 1951
*
1960
**
1969
*
1978 1987 1996 2005
****
2014
1971
*
1980
*
1989
*
1998
*
2007
**
2016
* Denoted a Category 5 hurricane in a given year.
The 56 year sequences are separated by an interval of 9 years.
Source of Raw Data: UNISYS.
Source: McMinn (2011c).
Volcanic Eruptions
Hawaii. The beginning of Kilauea and Mauna Loa eruptions was well documented by the
US Geological Survey (see Appendices 6 & 7 respectively). Combining these two sets of
data gave a total of 91 eruptive beginnings, of which 34 appeared in the 9/56 year grid as
presented in Table 6 (significant p < .01). It would have been curious to see if the
maximum intensity of Hawaiian eruptions could have been linked to the 9/56 year grid.
Unfortunately, such raw data was unavailable.
Table 6
9/56 YEAR CYCLE: HAWAIIAN ERUPTIONS 1820–2010
Year ending July 31
Sq
52
Sq
05
Sq
14
Sq
23
Sq
32
Sq
41
Sq
50
Sq
03
Sq
12
Sq
21
Sq
30
Sq
39
Sq
48
Sq
01 1828 1837 1846 1855 1864
#
1873
#
1821 1830 1839 1848 1857 1866
#
1875 1884
*
1893
#
1902 1911 1920
*#
1929
**
1868
**#
1877
**#
1886 1895 1904
##
1913 1922
*
1931
*
1940
#
1949
#
1958 1967 1976
*
1985
1924
***
1933 1942
#
1951 1960
**
1969
****
1978
*
1987 1996 2005
1980
*
1989 1998 2007
8
* Denoted the beginning of a Kilauea eruption.
# Denoted the beginning of a Mauna Lao eruption.
The 56 year sequences are separated by an interval of 9 years.
Years in bold contained the start of Hawaiian eruptions in the year ending July 31.
Source of Raw Data: US Geological Survey.
Much higher significance could be achieved if the 9/56 year grid was converted to one
with repeating intervals 9 - 27 - 9 - 27 years ….. on the horizontal and 56 years on the
vertical (denoted as a 9-27/56 year cycle). Kilauea and Mauna Loa experienced 27
eruptive beginnings within Table 7 (significant p < 10-5
).
Table 7
9-27/56 YEAR CYCLE:
BEGINNING OF HAWAIIAN ERUPTIONS 1820–2010
Year ending July 31
Sq 52 Sq 05 Sq 32 Sq 41
1848 + 9 1857 + 27
1868
**#
+ 9 1877
**#
+ 27 1904
##
+ 9 1913 + 27
1924
****
+ 9 1933 + 27 1960
**
+ 9 1969
****
+ 27
1980
*
1989
Continued…….
Sq 12 Sq 21 Sq 48 Sq 01
1828 + 9 1837 + 27 1864
#
+ 9 1873
#
1884
*
+ 9 1893
#
+ 27 1920
*#
+ 9 1929
**
1940
#
+ 9 1949
#
+ 27 1976
*#
+ 9 1985
1996 + 9 2005
* Denoted the beginning of an eruption at Kilauea.
# Denotes the beginning of an eruption at Mauna Lao.
Years presented in bold contained eruptions in the year ending July 31.
Source of Raw Data: US Geological Survey.
World Mega Eruptions. A 9/56 year cycle could not be established for the timing of
major world eruptions (VEI ≥ 5) since 1600, based on the listing by the Smithsonian
Institute (see Appendix 8). However, a 9-27/56 year grid was found to be significant. Of
the 34 mega eruptions listed by the Smithsonian Institute since 1600, 18 appeared in
Table 8 (significant p < .001). Five of the 6 events with VEI ≥ 6 fell in this pattern, the
9
anomaly being the 1991 Mt Pinatubo eruption. NB: Volcanic Explosivity Index (VEI)
gives the intensity of a particular eruption.
Table 8
9-27/56 YEAR CYCLE AND WORLD MEGA ERUPTIONS SINCE 1600 VEI ≥ 5
Based on a listing by the Smithsonian Institute
Year ending October 20 Sq
48
Sq
19
Sq
28
Sq
55
Sq
08
Sq
35
Sq
44
1600
0219
+27 1627 +9 1636 +27
1611 +9 1620 +27 1647 +9 1656 +27 1683 +9 1692 +27
1640
0731
+27 1667
0923
+9 1676 +27 1703 +9 1712 +27 1739
0819
+9 1748 +27
1696 +27 1725 +9 1732 +27 1759 +9 1768 +27 1795 +9 1804 +27
1752 +27 1779 +9 1788 +27 1815
0517
+9 1824 +27 1851 +9 1860 +27
1808 +27 1835
0120
+9 1844 +27 1871 +9 1880 +27 1907
0328
+9 1916 +27
1864 +27 1891 +9 1900 +27 1927 +9 1936 +27 1963
0317
+9 1972 +27
1920 +27 1947 +9 1956
0330
+27 1983 +9 1992 +27 2019 +9 2028
1976 +27 2003 +9 2012
Continued……
Sq
15
Sq
24
Sq
51
Sq
04
Sq
31
Sq
40
Sq
11
1603
1623 +9 1632
1631
1216
+27 1659
1607 +9 1616 +27 1643 +9 1652 +27 1679 +9 1688 +27 1715
1663
0813
+9 1672 +27 1699 +9 1708
1707
1216
+27 1735 +9 1744 +27 1771
1719 +9 1728 +27 1755
1017
+9 1764 +27 1791 +9 1800
0115
+27 1827
1775 +9 1784 +27 1811 +9 1820 +27 1847 +9 1856 +27 1883
0827
1831 +9 1840 +27 1867 +9 1876 +27 1903
1902
1024
+9 1912
0606
+27 1939
1887 +9 1896 +27 1923 +9 1932
0510
+27 1959 +9 1968 +27 1995
1943 +9 1952 +27 1979 +9 1988 +27 2015
1999 +9 2008 +27 2035
10
VEI ≥ 5 eruptions presented in Bold.
Dates denoted as YYYYMDD.
Abbreviation: VEI - Volcanic Explosivity Index.
Source of Raw Data: Smithsonian Institute. Global Volcanism Program.
Source: McMinn (2012).
Discussion
The obvious question emerges as to what causes the 9/56 year effect, especially as it
shows up in such varied phenomena. Excellent Moon Sun correlates can be produced
with any events that cluster within the 9/56 year grid. The lunar ascending node will be
sited in two segments approximately 180 degrees opposite on the ecliptic circle, WITH
NO EXCEPTIONS (1st and 2
nd harmonics). All events in a particular 56 year sequence
have the lunar ascending node sited in a narrow sector of the ecliptic circle WITH NO
EXCEPTIONS (1st harmonic). For events occurring at a similar time of year and within
the 9/56 year grid, the apogee point will be found in three ecliptic segments 120 degrees
apart WITH NO EXCEPTIONS (3rd
harmonic). Any events happening around the same
time of year and in the same 9 year subcycle will have apogee in the same sector of the
ecliptic WITH NO EXCEPTIONS (1st harmonic). These properties of the 9/56 year grid
arise from the very close alignments of several lunisolar cycles at 9.0 and 56.0 solar years
(see Appendix 9). Presumably lunisolar tidal harmonics triggered critical events, as the
Moon, Sun, ascending node and apogee were prime factors in terrestrial tides. The 9/56
year cycle illustrated the interconnectivity of various critical phenomena – financial
panics, earthquakes, hurricanes and eruptions. By implication, the Moon and Sun may be
far more influential in the timing of such events than was previously thought possible.
How lunisolar cycles activated critical events remained a mystery. In finance, the Moon
and Sun may be viewed as influencing mass physiological cycles of the general
population, which determine the prevailing collective mood and thus financial outcomes.
Hormone levels of animals and humans have been shown to fluctuate over the lunar
month (Endres Schaad, 2002; Zimecki, 2006). Cajochen et al (2013) established that
humans achieve 30% less deep sleep during the full Moon, which presumably would
affect human behavior. Various studies have also linked hormone levels to market trading
success (Chen et al, 2005; Coates & Hebert, 2008; Coates et al, 2009). Anyone who is
able to crack the Moon Sun code in finance will be able to make accurate market
forecasts years in advance. Such information will probably never be published given the
potential profits to be made.
In seismology and volcanology, the Moon Sun tides were postulated to trigger the build-
up of stress in the Earth’s crust. Numerous papers have been published correlating
lunisolar cycles with the timing of earthquakes and eruptions (Kokus, 2011). It is not a
question of if there is a Moon Sun effect in the timing of such events, but how pervasive
is this influence. Alas, the lunisolar mathematics involved with the timing of critical
events remained indecipherable. The forecasting of major seismic events remains limited,
until the problem can be solved.
11
This paper illustrates the necessity of studying cycles generally. A 9/56 year grid was
first established in finance, then extrapolated to seismic events, hurricanes and eruptions.
Without the input from market studies, it would be doubtful if a 9/56 year cycle would
have ever been detected in patterns of earthquakes, extreme tropical storms or volcanic
eruptions. Such calamitous events can be interconnected and have a massive impact in
terms of loss of life and financial outcomes. Financial strains caused by the 1906 Great
San Francisco quake directly contributed to the ensuing 1907 October banking panic
(Odell & Weidenmar, 2011). Similarly, the 1923 great Tokyo earthquake completely
devastated the city, causing over 100,000 deaths and huge economic losses. Severe
financial distress was again experienced in Japan following the March 2011 mega quake.
Tokyo is long overdue for another great quake and when it does occur panic will sweep
through the world financial system. Additionally, exceptional hurricane activity in 2005
left New Orleans in ruins, while many oil production platforms were wrecked in the Gulf
of Mexico causing severe disruption to US energy supplies. Any technique that can
accurately predict the timing of critical events would lessen their impact in terms of both
economic destruction and lives lost.
A 9/56 year cycle has been established for finance, earthquakes and Atlantic hurricanes
and all three phenomena have been linked to sunspot cycles. (The author knows of no
studies supporting a connection between sunspots and volcanic eruptions.)
Krivelyova & Robotti (2003) found that high geomagnetic storm activity induced stock
market declines the following week. The outcome was statistically and economically
significant. The size of the geomagnetic storm effect was similar within and across
countries, ranging between -0.77% and -4.4% of average annual returns. According to the
authors, substantially higher stock market returns were recorded during periods of quiet
geomagnetic activity.
Choi & Maslov (2010) established that earthquake frequency for the 1973-2010 period
was “closely related to the solar [sunspot] cycle: the number of earthquakes increases
during the declining/trough periods.” The authors also listed numerous additional
references on links between sunspot and earthquake cycles.
Hodges & Elsner (2010) showed that the likelihood of three or more hurricanes hitting
the US coast rises from 20% to 40% in years when sunspot activity is in the lowest 25%,
compared with years in the highest 25%. During peak sunspot years, there is only a 25%
chance of one or more hurricanes hitting the USA, a figure that spikes to 64% in the
lowest sunspot years.
How the 9/56 year lunisolar tidal effect and the sunspot cycle interact remained unknown.
Conclusions
The findings from the various assessments supported a 9/56 year cycle in the timing of:
* major financial panics in US & Western European history post 1760.
* major earthquakes in south western North America since 1800.
12
* Category 5 Atlantic hurricanes.
* the beginning of Hawaiian volcanic eruptions post 1820.
A 9-45/56 year cycle was also determined for world mega quakes since 1900, while a 9-
27/56 year cycle yielded high significance for the timing of world mega eruptions since
1600. Hawaiian tsunamis originating from Chile and Alaska may also occur
preferentially in 9/56 year grids (McMinn 2011d). The author has not examined a 9/56
year tsunami effect in much detail and it remained to be explored more fully.
Unfortunately, suitable raw data on major US tornadoes has only been available since
1950, which prevented an meaningful assessment of the 9/56 year effect.
The 9/56 year grids in Table 1 (financial panics), Table 5 (Category 5 Atlantic
hurricanes) and Table 6 (beginning of Hawaiian eruptions) were very similar, but they
each produced a different series of extreme events. The layout in Table 1 contained US
financial disasters in 1792, 1819, 1837, 1857, 1873, 1884, 1893, 1920, 1929, 1931, 1933,
1980, 1987, 1998 and 2007. The timing of Category 5 Atlantic hurricanes in Table 5
gave 1924, 1951, 1958, 1960, 1967, 1969, 1971, 1980, 1989, 1998, 2005 and 2007. The
beginning of Hawaiian eruptions in Table 6 happened in 1864, 1866, 1868, 1873, 1877,
1884, 1893, 1904, 1920, 1922, 1924, 1929, 1931, 1940, 1942, 1949, 1960, 1969, 1976,
1978 and 1980. The three series appeared to be random with no mathematical
interrelationships. However, they may be linked by very similar 9/56 year grids.
The 9/56 year tidal effect is hypothesized to arise from the varying angles between the
Moon, Sun, lunar ascending node, apogee and the spring equinox point. Diurnal cycles
could also be relevant, but they have not been considered in this paper. Lunisolar tidal
harmonics are the best options for further study. All too often researchers undertake
studies testing one Moon Sun factor (in academic finance this has always been lunar
phase). If no correlates were realized, then the Moon and Sun were considered to have no
impact. Unfortunately, the real situation is far more complicated.
If the Moon Sun mathematics can ever be deciphered, accurate predictions could be given
of windows when critical events were most likely to occur in the various disciplines -
finance, seismology, climatology and volcanology. However, current understanding of
the 9/56 year effect remained extremely limited. Hopefully this paper will assist in the
design of much needed follow up research.
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Krivelyova, A. & C Robotti, 2003. Playing The Field: Geomagnetic Storms &
International Stock Markets. Working Paper 2003-5b. Federal Reserve Bank of Atlanta.
http://www.frbatlanta.org/pubs/wp/working_paper_2003-5b.cfm?redirected=true
McMinn, David, 1986, The 56 Year Cycles & Financial Crises. 15th Conference of
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Aug 25-29.
McMinn, David, 1993. Financial Crises & The Number 56. The Australian Technical
Analysts Association Newsletter. p 21-25. September.
McMinn, David. 1996. Financial Crises & The Number 56. Cycles. The Foundation For
The Study of Cycles. p 11-17. Vol 46, No 1. August.
McMinn, David, 2002. 9/56 Year Cycle: Financial Crises.
http://www.davidmcminn.com/pages/fcnum56.htm
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Global Tectonics Newsletter. No 58. p 33-44. March.
McMinn, David, 2011b. 9/56 Year Cycle: Record Earthquakes. New Concepts In Global
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McMinn, David. 2012. 9/56 Year Cycle: World Mega Volcanic Eruptions. New
14
Concepts in Global Tectonics Newsletter. No 64. p 7-18. September.
Odell, Kerry & Weidenmar, Marc. 2011, Research Links the San Francisco
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http://weather.unisys.com/hurricane/atlantic/index.html.
US Geological Survey. Californian Earthquake History: 1769 to Present.
http://earthquake.usgs.gov/regional/sca/ca_eqs.php
US Geological Survey. Summary of Historical Eruptions, 1750 – Present.
http://hvo.wr.usgs.gov/kilauea/history/historytable.html
US Geological Survey. Summary of Historical Eruptions. 1843 – Present.
http://hvo.wr.usgs.gov/maunaloa/history/historytable.html
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http://www.ncbi.nim.nih.gov/pubmed/164007788
Appendix 1
THE 9/56 YEAR CYCLE AND LISTINGS OF FINANCIAL CRISES
Year beginning March 1
Source Era Total Appearing in
Table 1
Probability
Kindleberger (1996) 1760-1940 30 16 p < .001
1760-1996 44 21 p < .01
Kitchin (1933) 1796-1933 38 16 p < .05
Adams (1936) 1763-1933 31 15 p < .01
Encyclopedia
Americana (1995) 1672-1949 31 16 p < .001
Years *asterisked below appeared in the 9/56 year grid presented in Table 1.
Sources. Kindleberger (Appendix B 1996). 1760-1996. 1763*, 1772*, 1793 (Jan)*, 1797,
1799*, 1811 (Jan)*, 1815-1816, 1819*, 1825, 1828, 1836-1837*, 1838, 1847-1848*, 1857*,
1864 (Jan), 1866*, 1873*, 1882 (Jan), 1890, 1893*, 1907, 1920*-1921, 1929*, 1931*-1932-
1933*, 1958*, 1962, 1963, 1964, 1968, 1973, 1974-1975, 1979, 1980*, 1982, 1985*, 1987*,
1990 (Jan)* .
Adams (1936). US & Wn European crises 1760-1933: 1763*, 1772*, 1783*, 1793 (Jan)*,
1811 (Jan)*, 1817*-1818, 1825, 1837*, 1839*, 1847, 1857*, 1860, 1866*, 1873*, 1882
(Jan), 1883, 1889-1890, 1893*, 1900, 1903, 1907, 1910, 1914, 1920*, 1929*-1930-1931*,
1932-1933*.
Encyclopedia Americana (1995). Vol 21 p 358. US & Wn European crises 1672-1932:
1672 (Jan)*, 1692 (error - 1696* correct?), 1720, 1763*, 1793* (Jan 1793), 1825, 1836-
1837*, 1847, 1857*, 1866*, 1869, 1873*, 1882 (Jan), 1884*, 1889-1890, 1900, 1904*, 1907,
1914, 1920*, 1929*-1930-1931*-1932.
Vol 5, p 46-47. US crises 1837-1949: 1837*, 1873*, 1882, 1883, 1884*, 1893*, 1920*,
1929*-1930-1931*-1932-1933*, 1937, 1946, 1949*.
Kitchin (1933). Major US/Wn European crises 1796-1933: 1796, 1801*, 1810*, 1818, 1825,
15
1836, 1847, 1857*, 1866*, 1873*, 1881 (Jan 1882), 1890, 1900, 1907, 1913*, 1920*, 1929*-
1930-1931*-1932-1933*.
Minor US/Wn European crises 1799-1914: 1799*, 1805, 1814, 1831, 1839*, 1845, 1854,
1860-1861, 1863-1864*, 1870, 1875*, 1878, 1884*, 1893*, 1914.
Appendix 2
MAJOR EARTHQUAKES IN CALIFORNIA - NEVADA
- BAJA CALIFORNIA 1800–2010 (mag ≥ 6.9)
Year Mth Dy Mag Location
1812 12 08 7.0 Wrightwood
1812 12 21 7.0 Santa Barbara Channel
1838 06 ?? 7.0 San Francisco Peninsula
1857 01 09 8.25 Great Tejon earthquake
1868 10 21 7.0 Hayward Fault
1872 03 26 7.6 Owens Valley
1892 02 24 7.0 Laguna Salada, BC
1899 04 16 7.0 West of Eureka
1906 04 18 8.25 Great San Francisco quake
1915 10 03 7.3 Pleasant Valley, Nevada
1915 11 21 7.1 Volcano Lake, BC
1918 04 21 6.9 San Jacinto
1922 01 31 7.3 West of Eureka
1923 01 22 7.2 Cape Mendocino
1927 11 04 7.3 South West of Lompoc
1932 12 21 7.2 Cedar Mountain, Nevada
1934 12 31 7.0 Colorado River
1940 05 19 7.1 Imperial Valley
1952 07 26 7.7 Kern County
1954 12 16 7.1 Fairview Peak, Nevada
1980 11 08 7.2 West of Eureka
1989 10 18 7.1 Loma Prieta
1991 08 17 7.1 West of Crescent City
1992 04 25 7.2 Cape Mendocino
1992 06 28 7.3 Landers
1994 09 01 6.9 Mendocino Fracture Zone
1999 10 16 7.2 Hector Mine
2005 06 15 7.2 Offshore Northern California
2009 08 03 6.9 Baja California
2010 04 04 7.2 Mexicali, Baja California
2010 10 22 6.9 Baja California
Earthquakes in bold occurred in Table 2.
Main Source: US Geological Survey. Californian Earthquake History: 1769 to
Present. http://earthquake.usgs.gov/regional/sca/ca_eqs.php
16
Appendix 3
RECORD QUAKES IN SOUTH WESTERN NORTH AMERICA
Table 2 in the main text contained numerous records for south western North America. Many
additional events occurred in the 9/56 year grid as presented in Table A. These two grids
comprise 29% of the complete 9/56 year grid, but they contained all the record quakes for
California, Nevada, Arizona, New Mexico, Baja California, Sonora and Hawaii.
Sq 16 – Record quake for the Mexican state of Sonora (south of Arizona) (mag 7.5. May 3,
1887).
Sq 25 – 2nd
rank quake for southern California (Kern County. mag 7.7. Jul 26, 1952).
Sq 34 – Equal 1st rank for Arizona (Flagstaff. mag 6.2. Jan 25, 1906).
Sq 05 – 2nd
rank quake for Nevada (Cedar Mountain. mag 7.2. Dec 21, 1932).
Sq 41 – Record quake for southern California (Fort Tejon. mag 8.25. Jan 9, 1857).
Sq 41 – Equal 1st rank quake for Arizona (Lockett Tanks. mag 6.2. Aug 18, 1912).
Sq 50 – Equal 2nd
rank quake for northern California (west of Eureka. mag 7.3. Jan 31, 1922).
Sq 50 – 4th rank quake for Arizona (Freedonia. mag 5.5. Jul 21. 1959).
Sq 52 – Record quake for western USA (Great Cascadia quake. mag 9.0. Jan 26, 1700).
Table A Appendix 3
9/56 YEAR CYCLE: RECORD QUAKES IN
SOUTH WESTERN NORTH AMERICA 1850–2010
9 months ending January 31
Sq 16 Sq 25 Sq 34 Sq 43 Sq 52 Sq 05 Sq 14 Sq 23 Sq 32 Sq 41 Sq 50
1857
Jan09
1866
1850 1859 1868 1877 1886 1895 1904 1913
1912
Aug18
1922
Jan31
1888
1887
May03
1897 1906
Jan25
1915 1924 1933
1932
Dec21
1942 1951 1960
1959
Jul21
1969 1978
1944 1953
1952
Jul26
1962 1971 1980 1989 1998 2007
2000 2009
Record quakes mentioned in this appendix have been highlighted in bold.
Appendix 4
MAGNITUDES OF THE LARGEST SEISMIC EVENTS: 1900 – 2012
Kazuya Fujita (revised March 1, 2010)
Rank Date Location Mw
1a
1b
1c
1960.05.22
1960.05.22
1960.05.22
Chile Mainshock (a)
Chile "Precursor" (a)
Chile "Afterslip"(a)
9.6
9.5
9.0
2 1964.03.28 Prince William Sound, Alaska 9.2
17
3 2004.12.26 Offshore Northern Sumatra 9.0
4 1952.11.04 Kamchatka (Russia) 9.0
2011.03.11 Offshore Honshu Japan 9.0
2010.02.27 Bio Bio, Chile 8.8
5 1965.02.04 Aleutian Islands, Alaska 8.7
6 1950.08.15 Assam, India 8.7
7 1933.03.02 Sanriku, Japan 8.6
8 1957.03.09 Aleutian Islands Alaska 8.6
9 1906.01.31 Ecuador-Colombia 8.6
2005.03.28 Offshore Northern Sumatra 8.6
2012.04.11 Offshore Indonesia 8.6
10 1963.10.13 Etorofu, Kurile Islands 8.5
11 1938.02.01 Banda Sea, Indonesia 8.5
12 1906.08.17 Valparaiso, Chile 8.5
13 1923.02.03 Kamchatka 8.5
2007.09.12 Offshore southern Sumatra 8.5
(a) There were three mega earthquakes on May 22, 1960 (mag ≥ 9.0), but they have
been treated as one event.
Episodes (mag ≥ 8.5) post 2004 were sourced from the US Geological Survey and
inserted by the author.
Years in bold contained major quakes that took place within the 9/56 year grid as
presented in Table 4.
Sources: Fujita, K., Magnitudes of the Largest Events of the 20th Century.
www.msu.edu/~fujita/earthquake/bigquake.html
US Geological Survey., Historic World Earthquakes.
http://earthquake.usgs.gov/earthquakes/world/historical.php
Appendix 5
CATEGORY 5 ATLANTIC HURRICANES 1851–2009
Year Active Rank
(a)
Cat Year Active Rank
(a)
Cat
1924 Oct 14 – Oct 23 10 5 1971 Sep 05 – Sep 18 6 5
1928 Sep 06 – Sep 20 4 5 1977 Aug 29 – Sep 03 1 5
1932 Aug 30 – Sep 13 4 5 1979 Aug 25 – Sep 08 4 5
1935 Aug 29 – Sep 10 2 5 1980 Jul 31 – Aug 11 1 5
1938 Sep 10 – Sep 22 4 5 1988 Sep 08 – Sep 20 8 5
1947 Sep 04 – Sep 21 4 5 1989 Sep 10 – Sep 25 8 5
1950 Aug 30 – Sep 17 4 5 1992 Aug 16 – Aug 28 2 5
1951 Sep 02 – Sep 13 5 5 1998 Oct 22 – Nov 09 13 5
1955 Sep 21 – Sep 30 10 5 2003 Sep 06 - Sep 20 9 5
1958 Aug 11 – Aug 22 3 5 2004 Sep 02 – Sep 24 9 5
1960 Aug 29 - Sep 14
Sep 14 – Sep 17
5
6
5
5
2005 Jul 11 – Jul 21
Aug 23 – Aug 31
Sep 18 – Sep 26
5
11
17
5
5
5
18
Oct 15 – Oct 26 22 5
1961 Sep 03 – Sep 16
Oct 27 – Nov 01
3
9
5
5 2007 Aug 13 – Aug 23
Aug 31 – Sep 06
4
6
5
5
1967 Sep 05 – Sep 22 2 5
1969 Aug 14 – Aug 22 3 5
(a) In a given year, the first hurricane of the season is numbered 1, the second 2, the third 3 and so
forth.
Category 5 hurricanes in bold appear in Table 5.
Source of Raw Data: UNISYS. Atlantic Tropical Storm Tracking By Year.
http://weather.unisys.com/hurricane/atlantic/index.html
Appendix 6
BEGINNING OF KILAUEA ERUPTIONS SINCE 1820
Year Start Vol (km3) Year Start Vol (km3)
1983 Jan 03 1.9 1955 Feb 28 0.0876
1982 Sep 25 0.003 1954 May 31 0.0062
1982 Apr 30 0.0005 1952 Jun 27 0.0467
1979 Nov 16 0.00058 1934 Sep 06 0.0069
1977 Sep 13 0.0329 1931 Dec 23 0.007
1975 Nov 29 0.00022 1930 Nov 19 0.0062
1974 Dec 31 0.0143 1929 Jul 25 0.0026
1974 Sep 19 0.0102 1929 Feb 20 0.0014
1974 Jul 19 0.0066 1927 Jul 07 0.0023
1973 Nov 10 0.0027 1924 Jul 19 0.000234
1973 May 05 0.0012 1924 May 10 No lava
1972 Feb 03 0.162 1923 Aug 25 ? 0.000073
1971 Sep 24 0.0077 1922 May 28 ?
1971 Aug 14 0.0091 1921 Mar 18 0.0064
1969 May 24 0.185 1919 Dec 21 0.0453
1969 Feb 22 0.0161 1919 Feb 07 0.0252 ?
1968 Oct 07 0.0066 1918 Feb 23 0.000183
1968 Aug 22 0.00013 1894 Jul 07 ?
1967 Nov 05 0.0803 1894 Mar 21 ?
1965 Dec 24 0.00085 1885 Mar ?
1965 Mar 05 0.0168 1884 Jan 22 ?
1963 Oct 05 0.0066 1877 May 21 ? ?
1963 Aug 21 0.0008 1877 May 04 ?
1962 Dec 07 0.00031 1868 Apr 02 ? 0.000183
1961 Sep 22 0.0022 1868 Apr 02 ?
1961 Jul 10 0.0126 1840 May 30 0.205
1961 Mar 03 0.00026 1832 Jan 14 ?
1961 Feb 24 0.000022 1823 Feb Jul 0.0110
1960 Jan 13 0.1132
1959 Nov 14 0.0372
19
Eruptions in bold appeared in 9/56 year cycle in Table 6.
Source: US Geological Survey. Summary of Historical Eruptions, 1750 – Present.
http://hvo.wr.usgs.gov/kilauea/history/historytable.html
Appendix 7
BEGINNINGS OF MAUNA LOA ERUPTIONS SINCE 1840
Year Start Vol (km3) Year Start Vol (km
3)
1984 Mar 26 0.220 1892 Nov 30 0.012
1975 Jul 5 0.030 1887 Jan 16 0.128
1950 Jun 1 0.376 1880 Nov 5 0.130
1949 Jan 6 0.116 1880 May 1 0.130
1942 Apr 26 0.176 1879 Mar 9 0.001
1940 Apr 17 0.110 1877 Feb 14 0.008
1935 Nov 21 0.087 1872 Aug 9 0.630
1933 Dec 2 0.100 1871 Aug 10 0.020
1926 Apr 10 0.121 1868 Mar 27 0.123
1919 Sep 26 0.183 1865 Dec 30 0.050
1916 May 19 0.031 1859 Jan 23 0.383
1914 Nov 25 0.055 1855 Aug 8 0.280
1907 Jan 9 0.121 1852 Feb 17 0.182
1903 Oct 6 0.070 1851 Aug 8 0.035
1903 Sep 1 0.003 1849 May ? 0.025
1899 Jul 1 0.081 1843 Jan 10 0.202
1896 Apr 21 0.025
Eruptions in bold commenced in the 9/56 year grid as given in Table 6.
Source: US Geological Survey. Summary of Historical Eruptions, 1843 – Present.
http://hvo.wr.usgs.gov/maunaloa/history/historytable.html
Appendix 8
WORLD VOLCANIC MEGA ERUPTIONS SINCE 1600 VEI ≥ 5
Listing by the Smithsonian Institute
VEI DATE VOLCANO COUNTRY
6 1600 Feb 19 Huaynaputina Peru
5 1625 Sep 02 Katla Iceland
5? 1630 Sep 03 Furnas Azores
5 1631 Dec 16 Vesuvius Italy
5 1640 Aug 31 Komaga-Take Japan
5? 1641 Jan 04 Parker Philippines
5 1650 ± 10 yrs* Shiveluch Kamchatka Russia
6 1660 ± 20 yrs* Long Island Papua New Guinea
5 1663 Aug 16 Usu Japan
5 1667 Sep 23 Shikotsu Japan
5? 1673 May 20 Gamkokora Indonesia
20
5? 1680 ?? ?? Tongkko Indonesia
5 1707 Dec 16 Fuji Japan
5? 1721 May 11 Katla Iceland
5 1739 Aug 19 Shikotsu Japan
5? 1755 Oct 17 Katla Iceland
5 1800 Jan 15
± 120 days
Mt St Helens Washington USA
7 1815 May 10 Tombora Indonesia
5 1822 Oct 08 Galunggung Indonesia
5 1835 Jan 20 Cosiguina Nicaragua
5 1854 Feb 18 Shiveluch Kamchatka
5 1875 Mar 25 Askja Iceland
6 1883 Aug 27 Krakatau Indonesia
5 1886 Jan 11 Okataina New Zealand
6 1902 Oct 24 Santa Maria Guatemala
5 1907 Mar 28 Ksudach Kamchatka Russia
6 1912 Jun 06 Novarupta Alaska USA
5 1913 Jan 20 Colima Mexico
5 1932 Apr 10 Azul Cerro Chile
5 1933 Jan 08 Kharimkotan Kuriles Russia
5 1956 Mar 30 Bezymianny Kamchatka Russia
5 1963 Mar 17 Agung Lesser Sunda Is
5 1980 May 18 Mt St Helens Washington USA
6 1991 Jun 15 Mt Pinatubo Philippines
5 1991 Aug 12 Cerro Hudson Chile
* Imprecise date could not be used in the calculations.
Events in bold fell within the 9-27/56 year cycle as shown in Table 8.
Abbreviation: VEI - Volcanic Explosivity Index
Source: Smithsonian Institute. Global Volcanism Program. Large Holocene
Eruptions.
Appendix 9
MOON SUN BACKGROUND INFORMATION
Apogee Apogee is the point in the lunar orbit, where the Moon is the greatest distance from Earth, while
perigee is the least distance. In the lunar apse cycle, the apogee – perigee axis (apsides) rotates
counter clockwise around the ecliptic circle, with apogee completing one cycle from spring
equinox to spring equinox every 8.8474 tropical years. The apsides is very important in oceanic
tides on Earth. When the full/new Moon is at apogee, the amplitude of tides in New York Harbor
is 50% lower than when the full/new Moon is at perigee. Apogee could be expected to play a key
role in any Moon Sun tidal effect.
9.0 divided by the 8.8474 year apse cycle yielded 1.02, while 56.0 divided by the apse cycle gave
6.33 (6 plus one third). Thus, every 9.0 years apogee will be sited about 6 degrees further
anticlockwise on the ecliptic circle. Every 56.0 years, apogee will be located 120 degrees further
21
anticlockwise on the ecliptic circle. For events occurring around the same time of year in the 9/56
year grid, apogee is always located in three segments approximately 120 degrees apart on the
ecliptic circle. For example, Table A gives the apogee position as on July 1 of those years in a
9/56 year grid. Apogee was always located in three segments 120 degrees apart 335 – 015 Eo; 095
– 135 Eo and 215 – 250 E
o (3
rd harmonic).
Table A Appendix 9
9/56 YEAR CYCLE & THE POSITION OF APOGEE
Ecliptic Degree of Apogee on July 1
Sq 32 Sq 41 Sq 50 Sq 03 Sq 12 Sq 21
1763
000
1772
007
1781
013
1792
100
1801
106
1810
113
1819
119
1828
126
1837
131
1848
219
1857
225
1866
231
1875
237
1884
244
1893
250
1904
337
1913
344
1922
350
1931
356
1940
002
1949
008
1960
096
1969
102
1978
108
1987
115
1996
121
2005
127
The 56 year sequences are separated by an interval of 9 years.
Equinoxes
These points are sited where the plane of the Earth’s equator projected out onto the sky (celestial
equator) cuts the plane of the Earth’s orbit around the Sun (ecliptic). The vernal or spring equinox
(000 E°) occurs around March 20 and is sited where the Sun crosses the celestial equator from
south to north. The autumnal equinox (180 E°) happens around September 22 and is located
where the Sun crosses the celestial equator from north to south.
Lunar Ascending Node The lunar nodes are sited, where the plane of the Earth’s orbit around the Sun (the ecliptic) is cut
by the plane of the Moon’s orbit around the Earth. The ascending (north) node is where the Moon
crosses the ecliptic from south to north, whereas the descending (south) node is where the Moon
crosses from north to south. In the lunar nutation cycle, it takes 18.62 years for the ascending
node to complete one cycle from spring equinox to spring equinox.
The ecliptic position of the lunar ascending node in a 9/56 year grid is presented in Table B. On
July 1, this point is always found in two segments approximately 180 degrees apart in the ecliptic
circle (1st and 2
nd harmonics). In any particular 56 year sequence, the lunar node is always found
in a narrow sector of the ecliptic circle (1st harmonic).
Table B Appendix 9
9/56 YEAR CYCLE &
THE POSITION OF THE ASCENDING NODE
Ecliptic Degree of Ascending Node on July 1
Sq 32 Sq 41 Sq 50 Sq 03 Sq 12 Sq 21
22
1763
019
1772
205
1781
031
1792
178
1801
004
1810
190
1819
016
1828
202
1837
028
1848
175
1857
001
1866
187
1875
013
1884
199
1893
025
1904
172
1913
358
1922
184
1931
010
1940
196
1949
022
1960
169
1969
355
1978
181
1987
007
1996
193
2005
019
The 56 year sequences are separated by an interval of 9 years.
Moon Sun Cycles.
The 9/56 year effect arises due to a very close alignment of several lunisolar cycles at 9.0 and
56.0 solar years (see Table C). NB: The synodic month (or lunar month) is the time taken for the
Moon and Sun to complete one cycle new Moon to new Moon and is the basic time unit in the
cycles discussed in this appendix.
Relative angles between the Moon, Sun, ascending node and apogee repeat very closely every
223 synodic months (or one 18.0 year Saros). These angles will also recur in similar ecliptic
positions - plus about 11 degrees anticlockwise on the ecliptic circle every 223 synodic months.
223 synodic months divided by two gives the Half Saros of 111.5 synodic months. Every 9.0
tropical years, the Moon repeats the same angle to the ascending node, with the Sun 180 degrees
on the opposite side of the angular circle. The apogee - Sun angle is similar, while the Moon -
apogee angle changes in multiples of 60 degrees.
On the same date every 56 years, the lunar ascending node is located a further 3 E° clockwise on
the ecliptic circle (eg: as on July 1: 1761 at 48 E°; 1817 - 45 E°; 1873 - 42 E°; 1929 - 39 E°; 1985
- 36 E°). This reflects a close alignment between the 18.6 year lunar nutation cycle and the solar
year. Every 692.5 synodic months (or one 56.0 year cycle), the Sun forms the same angle to the
ascending node with the Moon 180 degrees on the opposite side of the angular circle. The relative
angles of apogee to the Moon, Sun and ascending node change in multiples of 60 degrees.
Table C Appendix 9
9 & 56 YEAR LUNISOLAR CYCLES
18.0 Year Saros
Days Years Lunisolar cycles
6,574.36 18.00 18.0 Tropical Years
6,585.78 18.03 19.0 Nodical Years
6,585.32 18.03 223.0 Synodic Months (Saros cycle)
6,584.51 18.03 241.0 Tropical Months
6,585.35 18.03 242.0 Nodical Months
6,585.55 18.03 239.0 Apogee Months
9.0 Year Half Saros
Days Years Lunisolar Cycles
3,287.18 9.00 9.0 Tropical Years
23
3,292.89 9.02 9.5 Nodical Years
3,292.66 9.02 111.5 Synodic Months (Half Saros cycle)
3,292.26 9.01 120.5 Tropical Months
3,292.68 9.02 121.0 Nodical Months
3,292.77 9.02 119.5 Apogee Months
56.0 Year Cycle
20,453.44 56.00 56.0 Tropical Years
20,450.58 55.99 59.0 Nodical Years
20,449.94 55.99 692.5 Synodic Months (56 Year Cycle)
20,450.23 55.99 748.5 Tropical Months
20,449.97 55.99 751.5 Nodical Months
20,450.06 55.99 742.17 Apogee Months
Synodic Month (or Lunar Month) is the interval between successive new
Moons and is equal to 29.5306 days.
Tropical Year (or Solar Year) is the time taken for the Sun to complete one
cycle of the ecliptic from spring equinox to spring equinox and is equal to
365.2422 days.
Tropical Month is the time taken for the Moon to complete one cycle of the
ecliptic from spring
equinox to spring equinox and is equal to 27.3216 days.
Nodical Month (or Draconic Month) is the time taken for the Moon to
complete one cycle from ascending node to ascending node and is equal to
27.2122 days.
Nodical Year (or Eclipse Year) is the time taken for the Sun to complete one
cycle from
ascending node to ascending node and is equal to 346.6201 days.
Apogee Month (or Anomalistic Month) is the time taken for the Moon to
complete one cycle from apogee to apogee and is equal to 27.5546 days.
Source: McMinn, 1996.
These cycles of 111.5 and 692.5 synodic months repeat the angles of 0 and 180 degrees between
the Moon, Sun and ascending node very closely. Angles involving apogee repeat in multiples of
about 60 degrees. Thus, any events clustering in a 9/56 year grid will have the lunar ascending
node in two sectors of the ecliptic approximately 180 degrees apart WITH NO EXCEPTIONS (1st
and 2nd
harmonics). Any events in a particular 56 year sequence will have the lunar ascending
node in a narrow sector of the ecliptic WITH NO EXCEPTIONS (1st harmonic). If the events
occur around the same time of year and in the 9/56 year grid, then apogee will be in three ecliptic
sectors 120 degrees apart WITH NO EXCEPTIONS (3rd
harmonic). If events occurred around the
same time of year and in a particular 9 year subcycle, they will have apogee in one sector of the
ecliptic circle WITH NO EXCEPTIONS (1st harmonic).
